You've accurately identified its best use, however, which is something most people miss. Allow me to explain.
There are two different cases to be made for storage and renewables in the context of the grid. The first is to help smooth out grid variability caused by any reason - it might be variability caused by a) fluctuating output demands on the energy system or b) the variability associated with changes in generating inputs such as we see with wind or solar.
The second case for storage is the wasted energy from renewables when they are producing energy in excess of demand.
Due to end users turning power switches on an off, we have had to deal with grid variability long before variable renewables were a factor in any sense; so, the first case is something we already deal with using a variety of strategies and technologies. When we add in wind and solar, we change the profile of the grid a bit, but it is important to recognize the the operating profile of the grid is significantly different than that of any single source of generation. Trust me, when a nuclear plant has a problem and shuts down rapidly and unexpectedly it is much more significant to the grid than when a wave of wind travels between wind farms.
The second case for storage is what is starting to drive storage - it presents a new expanding economic opportunity to 'buy low/sell high'. But again, there are different ways to capitalize on that opportunity to time shift that energy supply, the most notable of which is the impending expansion of battery electric autos for personal transportation.
Off grid use is exactly as your post describes.